a new car is purchased for 17900 dollars. the value of the car depreciates at 12.25% per year. what will the…

Explanation:

Step1: Identify the depreciation formula

The formula for exponential - decay is $A = P(1 - r)^t$, where $P$ is the initial value, $r$ is the rate of depreciation as a decimal, and $t$ is the number of years.

Step2: Convert the percentage to a decimal

Given $r = 12.25%=0.1225$, $P = 17900$, and $t = 10$.

Step3: Substitute the values into the formula

$A=17900\times(1 - 0.1225)^{10}=17900\times(0.8775)^{10}$.

Step4: Calculate $(0.8775)^{10}$

Using a calculator, $(0.8775)^{10}\approx0.27737$.

Step5: Calculate the value of $A$

$A = 17900\times0.27737\approx4964.92$.

Answer:

$4964.92$